Definition of Axiomatizable. Meaning of Axiomatizable. Synonyms of Axiomatizable

- model theory, a branch of mathematical logic, an elementary class (or axiomatizable class) is a class consisting of all structures satisfying a fixed first-order...
- well-formed formulas of a first-order language is (primitively) recursively axiomatizable. This result is not related to the well-known Craig interpolation theorem...
- axiomatizable, even when it is recursively axiomatizable. (Note that a logic is recursively enumerable if and only if it is recursively axiomatizable...
- omitting the multiplication operation entirely. The theory is com****bly axiomatizable; the axioms include a schema of induction. Presburger arithmetic is...
- theory for which there is an independent set of axioms is independently axiomatizable. Some authors say that σ is independent of T when T simply cannot prove...
- to construct, for any sufficiently powerful and consistent finitely axiomatizable system – such as necessary to axiomatize the elementary theory of arithmetic –...
- theory that can be axiomatized without schemata is said to be finitely axiomatizable. Two well known instances of axiom schemata are the: induction schema...
- considered fuzzy logic satisfies some obvious effectiveness property). Any "axiomatizable" fuzzy theory is recursively enumerable. In particular, the fuzzy set...
- \varphi } or T⊢¬φ{\displaystyle T\vdash \neg \varphi }). Recursively axiomatizable first-order theories that are consistent and rich enough to allow general...
- above are sufficient. Thus, Boolean algebra is said to be finitely axiomatizable or finitely based. Moreover, the number of equations needed can be further...